Question

Сумма площадей двух комнат равна 56 кв.м.. найдите площади этих комнат, если ширина первой комнаты в два раза больше длины второй, а ширина второй в 3 раза короче первой?

Answer 1

Решение в приложении.
ОТВЕТ 48 и 8 квадратных метров.

Answer 2

Problem Analysis

We are given that the sum of the areas of two rooms is 56 square meters. The width of the first room is twice the length of the second room, and the width of the second room is three times shorter than the width of the first room. We need to find the areas of these two rooms.

Solution

Let's assume the length of the second room is x meters.

According to the given information, the width of the first room is twice the length of the second room, so the width of the first room is 2x meters.

The width of the second room is three times shorter than the width of the first room, so the width of the second room is (1/3) * (2x) = (2/3)x meters.

To find the area of a rectangle, we multiply its length by its width. Therefore, the area of the first room is (2x) * x = 2x^2 square meters, and the area of the second room is (2/3)x * x = (2/3)x^2 square meters.

We are given that the sum of the areas of the two rooms is 56 square meters. Therefore, we can write the equation:

2x^2 + (2/3)x^2 = 56

To solve this equation, we can combine the like terms:

(6/3)x^2 + (2/3)x^2 = 56

(8/3)x^2 = 56

Now, we can solve for x^2 by multiplying both sides of the equation by 3/8:

x^2 = (56 * 3) / 8

x^2 = 21

Taking the square root of both sides, we find:

x = √21

Therefore, the length of the second room is approximately √21 meters.

To find the width of the first room, we can substitute this value of x into the equation for the width of the first room:

Width of the first room = 2x = 2 * √21

To find the width of the second room, we can substitute the value of x into the equation for the width of the second room:

Width of the second room = (2/3)x = (2/3) * √21

Finally, we can calculate the areas of the two rooms using the formulas for the area of a rectangle:

Area of the first room = (2x) * x = 2x^2

Area of the second room = (2/3)x * x = (2/3)x^2

Substituting the values of x into these formulas will give us the areas of the two rooms.

Calculation

Let's calculate the areas of the two rooms using the formulas derived above.

Length of the second room (x) = √21

Width of the first room = 2 * √21

Width of the second room = (2/3) * √21

Area of the first room = (2 * √21) * √21

Area of the second room = ((2/3) * √21) * √21

Simplifying these expressions will give us the final answers.

Answer

The length of the second room is approximately √21 meters. The width of the first room is approximately 2 * √21 meters. The width of the second room is approximately (2/3) * √21 meters. The area of the first room is approximately 2 * √21 * √21 square meters. The area of the second room is approximately (2/3) * √21 * √21 square meters.

Please note that the values provided above are approximate due to the use of the square root of 21.